Compressible turbulence in space and astrophysical plasmas. Analytical approach and in-situ data analysis for the solar wind

My thesis work is principally dedicated to the understanding of the role of compressibility in low frequency turbulence of space plasmas (the solar wind, the magnetosphere etc.) and astrophysical plasmas (interstellar molecular cloud, the core of a star etc.). Three new exact relations have been derived analytically in the framework of isothermal and polytropic hydrodynamic turbulence and for isothermal MHD turbulence. By using these relations, various universal scaling properties of compressible turbulence have been investigated. In addition, plausible phenomenologies have been proposed in order to theoretically reproduce different power-laws for the total energy power spectra which had been obtained in previous numerical simulations of compressible turbulence. A semi-qualitative distinction between sub-sonic and supersonic regimes of turbulence is hence concluded. In the second part, an analysis using THEMIS spacecraft data is also performed in a view to explaining the effect of the compressibility in the turbulence of the fast solar wind. (author)